Slowing Down the Speed of Light Applications of "Slow" and "Fast" Light

Transcription

1 Slowing Down the Speed of Light Applications of "Slow" and "Fast" Light Robert W. Boyd Institute of Optics and Department of Physics and Astronomy University of Rochester with Mathew Bigelow, Nick Lepeshkin, Aaron Schweinsberg, Petros Zerom, Giovanni Piredda, Zhimin Shi, Heedeuk Shin, and others. Presented at SPIE, July 2005.

2 Interest in Slow Light Intrigue: Can (group) refractive index really be 10 6? Fundamentals of optical physics Velocity of light and the historical development of physics Optical delay lines, optical storage, optical memories Implications for quantum information And what about fast light (v > c or negative)? Boyd and Gauthier, Slow and Fast Light, in Progress in Optics, 43, 2002.

3 Slow Light and Optical Buffers All-Optical Switch input ports switch output ports Use Optical Buffering to Resolve Data-Packet Contention slow-light medium But what happens if two data packets arrive simultaneously? Controllable slow light for optical buffering can dramatically increase system performance. Daniel Blumenthal, UC Santa Barbara; Alexander Gaeta, Cornell University; Daniel Gauthier, Duke University; Alan Willner, University of Southern California; Robert Boyd, John Howell, University of Rochester

4 Challenge/Goal Slow light in a room-temperature solid-state material. Solution: Slow light enabled by coherent population oscillations (a quantum coherence effect that is relatively insensitive to dephasing processes).

5 Slow Light in Ruby Need a large dn/dw. (How?) Kramers-Kronig relations: Want a very narrow absorption line. Well-known (to the few people how know it well) how to do so: Make use of spectral holes due to population oscillations. Hole-burning in a homogeneously broadened line; requires T 2 << T 1. 1/T 2 1/T 1 inhomogeneously broadened medium homogeneously broadened medium (or inhomogeneously broadened) PRL 90,113903(2003); see also news story in Nature.

6 Spectral Holes in Homogeneously Broadened Materials Occurs only in collisionally broadened media (T 2 << T 1 ) pump-probe detuning (units of 1/T 2 ) Boyd, Raymer, Narum and Harter, Phys. Rev. A24, 411, 1981.

7 Slow Light Experimental Setup Function Generator Argon Ion Laser or EO modulator Digital Oscilloscope 40 cm Reference Detector Signal Detector Ruby Pinhole 7.25-cm-long ruby laser rod (pink ruby)

8 Measurement of Delay Time for Harmonic Modulation P = 0.25 W 1.0 Delay (ms) P = 0.1 W solid lines are theoretical predictions Modulation Frequency (Hz) For 1.2 ms delay, v = 60 m/s and ng = 5 x 10 6

9 Gaussian Pulse Propagation Through Ruby µs 1.0 Normalized Intensity Input Pulse Output Pulse v = 140 m/s ng = 2 x Time (ms) No pulse distortion!

10 Matt Bigelow and Nick Lepeshkin in the Lab

11 Advantages of Coherent Population Oscillations for Slow Light Works in solids Works at room temperature Insensitive of dephasing processes Laser need not be frequency stabilized Works with single beam (self-delayed) Delay can be controlled through input intensity

12 Alexandrite Displays both Saturable and Reverse-Saturable Absorption Both slow and fast propagation observed in alexandrite Mirror Sites: 4 T 2 or 4 T 1 σ 2,m rapid Al, Cr σ 1,m rapid 2 E T 1,m = 260 µs 4 A 2 O Inversion Sites: Be 4 T 2 or 4 T 1 rapid 2 E a σ 1,i T 1,i ~ 50 ms 4 A 2 b Bigelow, Lepeshkin, and Boyd, Science 301, 200 (2003).

13 Inverse-Saturable Absorption Produces Superluminal Propagation in Alexandrite At 476 nm, alexandrite is an inverse saturable absorber Negative time delay of 50 ms correponds to a velocity of -800 m/s M. Bigelow, N. Lepeshkin, and RWB, Science, 2003

14 Numerical Modeling of Pulse Propagation Through Slow and Fast-Light Media Numerically integrate the paraxial wave equation A z 1 v g A t = 0 and plot A(z,t) versus distance z. Assume an input pulse with a Gaussian temporal profile. Study three cases: Slow light v g = 0.5 c Fast light v g = 5 c and v g = -2 c

15 Pulse Propagation through a Slow-Light Medium (ng = 2, vg = 0.5 c)

16 Pulse Propagation through a Fast-Light Medium (n g =.2, v g = 5 c)

17 Pulse Propagation through a Fast-Light Medium (n g = -.5, v g = -2 c)

18 Are these predictions physical? (We simply postulated a negative group velocity) Consider a causal medium, for which Re n and Im n obey KK relations Treat a gain doublet, which leads to superluminal effects* 2 x 10-8 n-1 0 refractive index -2 pulse spectrum g 0.4 gain x 10 7 detuning δ (Hz) * see also Chiao, Steinberg, Wang, Kuzmich, Gauthier, etc.

19 Superluminal Pulse Propagation through a Causal Medium χ ( ω) = A (ω 0 Δω) ω iγ + A (ω 0 + Δω) ω iγ pulse duration = 10 µs Γ = (2π) 0.25 khz A = 250 / s Δω = (2π) 100 MHz = half frequency separation of gain lines

20 Propagation of a Truncated Pulse through Alexandrite as a Fast-Light Medium normalized intensity output pulse input pulse time (ms) Smooth part of pulse propagates at group velocity Discontinuity propagates at phase velocity (information velocity)

21 Limits on the Time Delay Induced by Slow-Light Propagation Robert W. Boyd Institute of Optics, University of Rochester Daniel J. Gauthier Department of Physics, Duke University Alexander L. Gaeta Applied and Engineering Physics, Cornell Alan E. Willner ECE Dept, USC See also Phys. Rev. A 71, (2005)

22 Motivation: Maximum Slow-Light Time Delay Slow light : group velocities < 10-6 c! Proposed applications: controllable optical delay lines optical buffers, true time delay for synthetic aperture radar. Key figure of merit: normalized time delay = total time delay / input pulse duration information storage capacity of medium Best result to date: delay by 4 pulse lengths (Kasapi et al. 1995) But data packets used in telecommunications contain 10 3 bits What are the prospects for obtaining slow-light delay lines with 10 3 bits capacity?

23 Review of Slow-Light Fundamentals L group velocity: v g = c n g group index: n g = n + ω dn dω group delay: T g = L v g = Ln g c slow-light medium, n g >> 1 controllable delay: T del = T g L/c = L c (n g 1) To make controllable delay as large as possible: make L as large as possible (reduce residual absorption) maximize the group index

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29 Modeling of Slow-Light Systems We conclude that there are no fundamental limitations to the maximum fractional pulse delay [1]. Our model includes gvd and spectral reshaping of pulses. However, there are serious practical limitations, primarily associated with residual absorption. Another recent study [2] reaches a more pessimistic (although entirely mathematically consistent) conclusion by stressing the severity of residual absorption, especially in the presence of Doppler broadening. Our challenge is to minimize residual absorption. [1] Boyd, Gauthier, Gaeta, and Willner, Phys. Rev. A 71, , [2] Matsko, Strekalov, and Maleki, Opt. Express 13, 2210, 2005.

30 Slow Light via Coherent Population Oscillations E 3, ω + δ E 1, ω saturable medium ω + δ measure absorption 2γ ba = 2 T 2 b Γ ba = 1 T 1 a absorption profile 1/T 1 Ground state population oscillates at beat frequency δ (for δ < 1/T 1 ). Population oscillations lead to decreased probe absorption (by explicit calculation), even though broadening is homogeneous. Rapid spectral variation of refractive index associated with spectral hole leads to large group index. Ultra-slow light (ng > 10 6 ) observed in ruby and ultra-fast light (n g = 4 x 10 5 ) observed in alexandrite by this process. Slow and fast light effects occur at room temperature! PRL 90,113903(2003); Science, 301, 200 (2003)

31 Prospects for Large Fractional Delays Using CPO ω + δ ω collection of two-level atoms ω + δ Strong pumping leads to high transparency, large bandwidth, and increased fractional delay. maximum delay in pulse widths = 0 T1/T2 = 100 Maximum fractional delay Rabi frequency times T1 ω probe absorption group index /ω T Absorption ΩT 1 = 40 ΩT 1 = 2 = 0 T 1 /T 2 = 100 ΩT 1 = 5 ΩT 1 = 10 ΩT 1 = δ T 1 Group index = 0 T 1 /T 2 = 100 ΩT 1 = 20 ΩT 1 = 10 ΩT 1 = 5 ΩT 1 = 2 ΩT 1 = 40 Boyd et al., Laser Physics δ T 1

32 Summary There are no fundamental limitations to the maximum normalized pulse delay. However, there are serious practical limitations, primarily associated with residual absorption. To achieve a longer fractional delay saturate deeper to propagate farther Exciting possibilities exist for optical buffering and other photonics applications if normalized time delays in the range of can be achieved. Next: Find material with faster response (semiconductors?) (to allow delay of shorter pulses)

33 Some New Results

34 Slow and Fast Light in an Erbium Doped Fiber Amplifier Fiber geometry allows long propagation length Saturable gain or loss possible depending on pump intensity Output Advance = 0.32 ms Input FWHM = 1.8 ms 0.15 Time 6 ms Fractional Advancement mw mw mw mw mw - 0 mw in out Modulation Frequency (Hz)

35 Slow-Light via Stimulated Brillouin Scattering Rapid spectral variation of the refractive response associated with SBS gain leads to slow light propagation Supports bandwidth of 100 MHz, group index of about 100 Even faster modulation for SRS Joint project with Gaeta and Gauthier Diode Laser Fiber Amplifier Oscilloscope typical data SBS Generator Polarization Control Circulator Variable Attenuator 50/50 Circulator Detector Modulator Isolator Pulse Generator RF Amplifier SBS Amplifier in out PRL 94, (2005).

36 Thank you for your attention. And thanks to NSF and DARPA for financial support!